= Ramsey ensemble coherence
{c}
{title2=$\chi(T)=\langle e^{i\eta T}\rangle$}
For an ensemble with static detunings $\delta+\eta$, ideal same-phase quarter-turn pulses give $\overline p_2(T)=[1+\operatorname{Re}(e^{i\delta T}\chi(T))]/2$. Here $\chi$ is the <characteristic function> of the offset distribution. A mean-zero Gaussian of RMS width $\sigma$ gives $\chi=e^{-\sigma^2T^2/2}$; a symmetric uniform interval gives a <sinc function>. A width alone does not uniquely specify the envelope.
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